elizahami7462 elizahami7462
  • 22-03-2021
  • Mathematics
contestada

Triangle ABC above has side a = 1 and side c = 2. What constraints does the triangle inequality theorem put on side b?

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MrRoyal
MrRoyal MrRoyal
  • 27-03-2021

Answer:

[tex]3 > b[/tex]

Step-by-step explanation:

Given

[tex]a = 1[/tex]

[tex]c = 2[/tex]

Required

Inequality to measure the length of b

The triangle inequality theorem states that:

[tex]a + b > c[/tex]

[tex]a + c > b[/tex]

[tex]b + c > a[/tex]

On side b, we make use of:

[tex]a + c > b[/tex]

Substitute values for a ad c

[tex]1 + 2 > b[/tex]

[tex]3 > b[/tex]

The inequality is: [tex]3 > b[/tex]

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